Qualitative meta-analysis on the hospital task: Implications for research

Journal of Statistics Education

Volumn 22, Issue 2, 2014, Pages

  Noll, Jennifer ^a   Sharma, Sashi ^b  

^a PORTLAND STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WAIKATO   (New Zealand)

Author keywords

Sample size; Sampling distributions; Statistical reasoning; The law of large numbers; Variability

Indexed keywords

EID: 84905101863     PISSN: None     EISSN: 10691898     Source Type: Journal    
DOI: 10.1080/10691898.2014.11889704     Document Type: Article

References (37)

1. Bar-Hillel, M. (1982). "Studies of Representativeness". In D. Kahneman, P. Slovic, and Tversky (eds.), Judgment Under Uncertainty: Heuristics and Biases, Cambridge University Press, New York.
2. Ben-Zvi, D. (2004). "Reasoning About Variability in Comparing Distributions". Statistics Education Research Journal, 3(2), 4-6.
3. Evans, J. St B. T., and Dusoir, A. E. (1977). "Proportionality and Sample Size as Factors in Intuitive Statistical Judgement". Acta Psychologica, 41, 129-137.
4. Evans, J. St B. T., and Pollard, P. (1982). "Statistical Judgement: A Further Test of the Representatives Construct". Acta Psychologica, 51, 91-103.
5. Falk, R., and Konold, C. (1992). "The Psychology of Learning Probability". In F. Sheldon and G. Sheldon (eds.), Statistics for the Twenty-First Century, pp. 151-164, Washington: Mathematical Association of America.
6. Fischbein, E., Nello, M. S., and Marino, M. S. (1991). "Factors Affecting Probabilistic Judgements in Children and Adolescents". Educational Studies in Mathematics, 22, 523-549.
7. Fischbein, E., and Schnarch, D. (1997). "The Evolution with Age of Probabilistic, Intuitively Based Misconceptions". Journal for Research in Mathematics Education, 28, 96-105.
8. Garfield, J.B., and Ben-Zvi, D. (2008). "Preparing School Teachers to Develop Students Statistical Reasoning". In C. Batanero, G. Burrill, C. Reading & A. Rossman (eds.), Joint ICMI/IASE Study: Teaching Statistics in School Mathematics, Challenges for Teaching and Teacher Education, Proceedings of the ICMI Study 18 and 2008 IASE Roundtable Conference
9. Gigerenzer, G. (1996). "On Narrow Norms and Vague Heuristics: A Rebuttal to Kahneman and Tversky". Psychological Review, 103, 592-6.
10. Gravemeijer, K. (1998). "Developmental Research as a Research Method. In Mathematics Education as a Research Domain: A Search for Identity, pp. 277-295, Springer. Retrieved from http://link.springer.com/chapter/10.1007/978-94-011-5470-3_18
11. Gravemeijer, K., and Cobb, P. (2006). "Design research from a Learning Design Perspective". Educational Design Research, 17-51.
12. Greer, B. (2001). "Understanding Probabilistic Thinking: The legacy of Efraim Fischbein". Educational Studies in Mathematics, 45, 15-53.
13. Greer, G., and Mukhopadhyay, S. (2005). "Teaching and Learning the Mathematization of Uncertainty: Historical, Cultural, Social and Political Contexts". In G. A. Jones (ed.), Exploring Probability in School: Challenges for Teaching and Learning, pp. 297-324, New York: Springer
14. Jones, G. A., Langrall, C. W., and Mooney, E. S. (2007). "Research in Probability: Responding to Classroom Realities". In F. K. Lester Jr (ed.), Second Handbook of Research on Mathematics Teaching and Learning, pp. 909-955, Reston: The National Council of Teachers of Mathematics
15. Kahneman, D., and Tversky, A. (1972). "Subjective Probability: A Judgment of Representativeness". Cognitive Psychology, 3, 430-454.
16. Kahneman, D., and Tversky, A. (1982). "Variants of Uncertainty". In D. Kahneman, P. Slovic, & A. Tversky (eds.), Judgment Under Uncertainty: Heuristics and Biases, pp. 509-521, New York: Cambridge University Press.
17. Konold, C. (1989). "An Outbreak of Belief in Independence?". In C. Maher, G. Goldin & B. Davis (eds.), The Proceedings of the Eleventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol II (pp. 203-209). Rutgers, Rutgers University Press.
18. Konold, C. (1991). "Understanding Students' Beliefs about Probability. "In E. von Glasersfeld (ed.), Constructivism in Mathematics Education, pp. 139-156, Dordrecht, The Netherlands: Kluwer.
19. Lubienski, S. (2002). "Research, Reform, and Equity in US Mathematics Education". Mathematical Thinking and Learning, 4(2/3), 103-125.
20. Miles, M. B., and Huberman, A. M. (1994), Qualitative Data Analysis: An Expanded Sourcebook, (2nd ed.). Thousand Oaks, CA: Sage Publications.
21. Nasir, N. S., Hand, V., and Taylor, E. V. (2008). "Culture and Mathematics: Boundaries between "Cultural" and "Domain" Knowledge in the Mathematics Classroom and Beyond". Review of Research in Education, 32, 187-240.
22. Noll, J. (2007), Graduate Teaching Assistants' Statistical Knowledge for Teaching. Unpublished doctoral dissertation from Portland State University.
23. Noll, J. (2011). "Graduate Teaching Assistants' Statistical Content Knowledge of Sampling". Statistics Education Research Journal, 10(2), 27-47.
24. Raeburn, R. (2008). "The Hospital Problem Revisited. Tertiary Student's Perceptions of a Problem Involving the Binomial Distribution". In M. Goos, R. Brown, and K. Makar (eds.) Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, © MERGA Inc. 2008
25. Rubin, A., Bruce, B., and Tenney, Y. (1991)". Learning about Sampling: Trouble at the Core of Statistics". In D. Vere-Jones (ed.), Proceedings of the Third International Conference on Teaching Statistics. Vol. 1. School and General Issues, pp. 314-319, Voorburg, The Netherlands: International Statistical Institute.
26. Saldanha, L., and Thompson, P. (2003), Conceptions of Sample and their Relationship to Statistical Inference. Educational Studies in Mathematics, 51, 257-270.
27. Saldanha, L., and Thompson, P. (2007). "Exploring Connections Between Sampling Distributions and Statistical Inference: An Analysis of Students' Engagement and Thinking in the Context of Instruction Involving Repeated Sampling". International Electronic Journal of Mathematics Education, 2, (3), www.iejme.com
28. Sedlmeier, P. (1998). "The Distribution Matters: Two Types of Sample-size Tasks". Journal of Behavioral Decision Making, 11, 281-301.
29. Sedlmeier, P., and Gigerenzer, G. (1997). "Intuitions about Sample Size: The Empirical Law of Large Numbers". Journal of Behavioral Decision Making, 10, 33-51.
30. Sharma, S. (1997). "Statistical Ideas of High School Students: Some Findings from Fiji". Unpublished doctoral thesis. Waikato University, Hamilton, New Zealand.
31. Shaughnessy, J. M. (2007). "Research on Statistics Learning and Leasoning". In F. K. Lester (Jr ed.), Second Handbook of Research on Mathematics Teaching and Learning, pp 957-1009, Reston: The National Council of Teachers of Mathematics.
32. Stavy, R., and Tirosh, D. (2000), How Students (Mis-)Understand Science and Mathematics Intuitive Rules, New York: Teachers College Press.
33. Stohl, H., and Tarr, T. J. (2002). "Developing Notions of Inference using Probability Simulation Tools". Journal of Mathematical Behavior, 21, 319-337.
34. Tversky, A., and Kahneman, D. (1974). "Judgement Under Uncertainty: Heuristics and Biases". Science, 185, 1124-1131.
35. Watson, J. M. (2000). "Preservice Mathematics Teachers' Understanding of Sampling: Intuition or Mathematics", Mathematics Teacher Education and Development, 2, 121-135.
36. Watson, J. M., and Moritz, J. B. (2000). "Developing Concepts of sampling". Journal for Research in Mathematics Education, 31(1), 44-70.
37. Well, A. D., Pollatsek, A., and Boyce, S. J. (1990). "Understanding the Effects of Sample Size on the Variability of the Mean". Organizational Behavior and Human Decision Processes, 47, 289-312.